1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
satela [25.4K]
3 years ago
7

The two linear functions are shown below f(x)=5/6x+3 what is true ?

Mathematics
1 answer:
Deffense [45]3 years ago
8 0
What are the two functions?
You might be interested in
More Calculus! (I'm so sorry)
Olenka [21]
Recall that converting from Cartesian to polar coordinates involves the identities

\begin{cases}y(r,\phi)=r\sin\phi\\x(r,\phi)=r\cos\phi\end{cases}

As a function in polar coordinates, r depends on \phi, so you can write r=r(\phi).

Differentiating the identities with respect to \phi gives

\begin{cases}\dfrac{\mathrm dy}{\mathrm d\phi}=\dfrac{\mathrm dr}{\mathrm d\phi}\sin\phi+r\cos\phi\\\\\dfrac{\mathrm dx}{\mathrm d\phi}=\dfrac{\mathrm dr}{\mathrm d\phi}\cos\phi-r\sin\phi\end{cases}

The slope of the tangent line to r(\phi) is given by

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\phi}}{\frac{\mathrm dx}{\mathrm d\phi}}=\dfrac{\frac{\mathrm dr}{\mathrm d\phi}\sin\phi+r\cos\phi}{\frac{\mathrm dr}{\mathrm d\phi}\cos\phi-r\sin\phi}

Given r(\phi)=3\cos\phi, you have \dfrac{\mathrm dr}{\mathrm d\phi}=-3\sin\phi. So the tangent line to r(\phi) has a slope of

\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{-3\sin^2\phi+3\cos^2\phi}{-3\sin\phi\cos\phi-3\cos\phi\sin\phi}=\dfrac{3\cos2\phi}{-3\sin2\phi}=-\cot2\phi

When \phi=120^\circ=\dfrac{2\pi}3\text{ rad}, the tangent line has slope

\dfrac{\mathrm dy}{\mathrm dx}=-\cot\dfrac{4\pi}3=-\dfrac1{\sqrt3}

This line is tangent to the point (r,\phi)=\left(-\dfrac32,\dfrac{2\pi}3\right) which in Cartesian coordinates is equivalent to (x,y)=\left(\dfrac34,-\dfrac{3\sqrt3}4\right), so the equation of the tangent line is

y+\dfrac{3\sqrt3}4=-\dfrac1{\sqrt3}\left(x-\dfrac34\right)

In polar coordinates, this line has equation

r\sin\phi+\dfrac{3\sqrt3}4=-\dfrac1{\sqrt3}\left(r\cos\phi-\dfrac34\right)
\implies r=-\dfrac{3\sqrt3}{2\sqrt3\cos\phi+6\sin\phi}

The tangent line passes through the y-axis when x=0, so the y-intercept is \left(0,-\dfrac{\sqrt3}2\right).

The vector from this point to the point of tangency on r(\phi) is given by the difference of the vector from the origin to the y-intercept (which I'll denote \mathbf a) and the vector from the origin to the point of tangency (denoted by \mathbf b). In the attached graphic, this corresponds to the green arrow.

\mathbf b-\mathbf a=\left(\dfrac34,-\dfrac{3\sqrt3}4\right)-\left(0,-\dfrac{\sqrt3}2\right)=\left(\dfrac34,-\dfrac{\sqrt3}4\right)

The angle between this vector and the vector pointing to the point of tangency is what you're looking for. This is given by

\mathbf b\cdot(\mathbf b-\mathbf a)=\|\mathbf b\|\|\mathbf b-\mathbf a\|\cos\theta
\dfrac98=\dfrac{3\sqrt3}4\cos\theta
\implies\theta=\dfrac\pi6\text{ rad}=30^\circ

The second problem is just a matter of computing the second derivative of \phi with respect to t and plugging in t=2.

\phi(t)=2t^3-6t
\phi'(t)=6t^2-6
\phi''(t)=12t
\implies\phi''(2)=24

6 0
3 years ago
Write an expression for the sequence of operations described below.
Anna [14]

Answer:

a - (6-9)

Hopefully this is correct

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
4(3-2x)=15 please helppp
mestny [16]

Answer:

x = -3/8

Step-by-step explanation:

4(3-2x)=15

Distribute

12 -8x = 15

Subtract 12 from each side

12-8x-12 = 15-12

-8x =3

Divide each side by -8

-8x/-8 = 3/-8

x = -3/8

7 0
3 years ago
Read 2 more answers
The 300 people who were lined up outside the amusement park had all entered by 8:15 a.m. By 8:30, 550 more had entered. The numb
Tasya [4]

Answer:

250; p= 300 + \frac{50}{3}t

Step-by-step explanation:

a. 15 minutes passed, so there would be 250 people who came in

b. You would create a formula, where t = time after 8:15 (in minutes), while p = people who are at the parade

300 + \frac{250}{15}t = p, which equals p= 300 + \frac{50}{3}t

7 0
3 years ago
Please I need help with some geometry. An image with the question is attached.
Vladimir [108]

Answer:

Not enough information

Step-by-step explanation:

You gave the height, but there is no length. You need both the height and length because the area of a triangle is 1/2bh

4 0
3 years ago
Other questions:
  • Write equivalent fractions for 3/5 and 1/3 that could be used to find the sum of the fractions
    15·1 answer
  • If you are given a 4% raise and inflation is 1%, you are___
    12·1 answer
  • Simplify the product: (4wx6)4 (wx)5
    11·1 answer
  • When I divide both sides of an inequality by a negative number, I notice...
    9·2 answers
  • Which statement best explains why the Exodus is an important event in the Jewish religion?
    5·1 answer
  • This exact same question has been asked a few times, but I’m finding several different answers. Could someone please clarify.
    13·2 answers
  • A cola container is in the shape of a right cylinder. The radius of the base is 4 centimeters, and the height is 12 centimeters.
    5·2 answers
  • Which Question is equivalent to
    14·2 answers
  • What is the first step
    7·2 answers
  • Identify the function shown in this graph
    8·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!